Problem: Calculate the product below and give your answer in scientific notation. $ {\left(5.2\times 10^{-2} \right) \times \left(8.0\times 10^{-4} \right) =\ ?} $
Answer: Start by collecting the significands and exponents. $ ({5.2} \times {10^{-2}}) \times ({8.0} \times {10^{-4}}) = ({5.2} \times {8.0}) \times ({10^{-2}} \times {10^{-4}}) $ Then multiply each term separately. When multiplying exponents with the same base, add the powers together. $= {41.6} \times {10^{-2 \,+\, -4}}$ $= {41.6} \times {10^{-6}}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$. In this case, we need to move the decimal one position to the left without changing the value of our answer. We can use the fact that ${41.6}$ is the same as ${4.16 \times 10}$ or ${4.16 \times 10^{1}}$. $ = {4.16 \times 10^{1}} \times {10^{-6}} $ $ = 4.16 \times 10^{{1} + {-6}} $ $= 4.16\times 10^{-5}$